White 111 vs Black 562
White starts from setup 111 (QNRNKRBB), Black from setup 562 (BRNKNBRQ). In the encyclopedia since 2026-10-15: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
How to play with different setups
White sets up the pieces by position No. 111, Black by position No. 562, mirrored on their own side; the pawns stand as usual.
Moves as usual: White starts; everything else follows the Chess960 rules.
The two setups
White: setup #111 Q N R N K R B B
King on the e-file, rooks on c, f, queen on the a-file; one bishop starts in a corner; the knights start on central files. Castling follows the Chess960 rule: king and rook end on the classical squares. In ordinary symmetric play setup 111 gives White +0.49 (Morozov Balance Index, 400M nodes).
Black: setup #562 B R N K N B R Q
King on the d-file, rooks on b, g, queen on the h-file; one bishop starts in a corner; the knights start on central files. Castling follows the Chess960 rule: king and rook end on the classical squares. In ordinary symmetric play setup 562 gives White +0.24 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation is exactly 0.00 each time, reaching search depth 57.
Admission rule: |cp| ≤ 5 at four budgets up to 4 billion nodes, no one-sided drift along the ladder, and confirmation by two independent engines — Berserk and Lc0 — each below its own median on symmetric positions. The same corridor is required at every deeper budget (8 G, 16 G) at which the pair has been evaluated.
The shallow rungs wandered between +2 and +36 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 111 gives White +0.49 and setup 562 gives White +0.24: with both sides on the same rank the first move is worth something. In this pair Black's own setup absorbs that edge completely.
The engine's first choice for White is g3; the alternatives are slightly weaker but keep the game level.
Along the engine's main line (30 moves) the evaluation stayed within ±29 cp the whole way: the balance holds as the pieces come out, not only on move one.
Engine self-play agrees: 10 games, White won 0, drawn 10, Black won 0 (White scored 50.0%).
Verification ladder
Nine independent searches of the starting position, each with a larger node budget. Evaluation in centipawns from White's point of view.
| Stage | Nodes | Depth | Eval, cp | Main line |
|---|---|---|---|---|
| S0 | 100 000 | 19 | +13 | 1. g3 g5 2. c4 h5 3. Nbc3 e6 4. Qb1 f5 |
| S1 | 500 000 | 20 | +2 | 1. g3 g5 2. c4 f5 3. Nbc3 e6 4. Qb1 Ne7 |
| S2 | 2 000 000 | 23 | +36 | 1. g3 g5 2. Ndc3 h5 3. O-O-O e6 4. a4 f5 |
| S3 | 8 000 000 | 29 | +29 | 1. g3 g5 2. a4 h5 3. Ndc3 e6 4. O-O-O f5 |
| S4 | 32 000 000 | 34 | +17 | 1. g3 e6 2. f4 f5 3. Nf2 g5 4. fxg5 Rxg5 |
| S5 | 128 000 000 | 39 | +3 | 1. g3 g5 2. Ndc3 e6 3. d3 h5 4. Nd2 f5 |
| S6 | 400 000 000 | 47 | 0 | 1. g3 g5 2. a4 e6 3. c4 b6 4. Bxa8 Rxa8 |
| S7 | 800 000 000 | 50 | 0 | 1. g3 g5 2. a4 e6 3. Ndc3 h5 4. O-O-O h4 |
| S8 | 1 600 000 000 | 57 | 0 | 1. g3 g5 2. Ndc3 h5 3. a4 e6 4. O-O-O h4 |
Deep verification
The search ladder reaches 1.6 billion nodes; admission needs a 4-billion rung and two further engines on top of that. Beyond even that, every pair was re-checked at budgets up to ten times larger and in thousands of self-play games. This section shows what each check returned for this pair.
| Nodes | Eval, cp |
|---|---|
| 4 000 000 000 | 0 |
| 8 000 000 000 | not checked |
| 16 000 000 000 | not checked |
This pair stays within the ±5 cp corridor up to 4 000 000 000 nodes.
Independent engines, run on the same position:
- Berserk 14: -3
- Lc0 0.32.1: -5
Independent confirmations: 3 of 3. An engine counts as confirming when its reading of the pair is closer to equality than its own reading of a typical symmetric Chess960 position (+10 for Berserk, +18 for Lc0). Where only one engine confirms, the pair is balanced according to that engine alone, and this page says so.
Own weight of each setup, measured against the classical array: White 0, Black +110, difference -110. A balanced pair needs White's setup to be weaker by about the price of the first move.
Extended self-play: 10 games, 0 White wins, 10 draws, 0 Black wins, White scored 50.0%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | 0 | 40 | 1. g3 g5 2. Ndc3 e6 3. a4 h5 4. O-O-O h4 5. d3 f5 |
| 2 | -31 | 40 | 1. b3 b6 2. f3 e6 3. g3 Ne7 4. e4 h5 5. Nf2 g5 |
| 3 | -37 | 40 | 1. a4 b6 2. f3 g6 3. e4 c5 4. g3 Bg7 5. f4 f5 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 29 cp, mean 4.9 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | g3 | +29 | g5 | +12 |
| 2 | a4 | -8 | e6 | +10 |
| 3 | Ndc3 | +4 | h5 | 0 |
| 4 | Qa2 | -8 | h4 | -21 |
| 5 | g4 | -18 | h3 | -17 |
| 6 | O-O-O | -15 | Nf6 | -3 |
| 7 | d4 | +6 | Nxg4 | +18 |
| 8 | d5 | +20 | Bd6 | +18 |
| 9 | Nb5 | +25 | b6 | +17 |
| 10 | N1c3 | +11 | a6 | +13 |
| 11 | Nxd6 | +17 | Nxd6 | +1 |
| 12 | Kb1 | 0 | Ne5 | 0 |
| 13 | f4 | -5 | gxf4 | 0 |
| 14 | Rxf4 | 0 | Qh6 | 0 |
| 15 | Be3 | 0 | Rg2 | 0 |
| 16 | dxe6 | 0 | fxe6 | 0 |
| 17 | Rxd6 | 0 | cxd6 | 0 |
| 18 | Qa3 | 0 | Nf7 | 0 |
| 19 | Nb5 | 0 | axb5 | 0 |
| 20 | Rxf7 | 0 | b4 | 0 |
| 21 | Qd3 | 0 | Qh4 | 0 |
| 22 | Bxg2 | 0 | hxg2 | 0 |
| 23 | Qxd6 | 0 | O-O-O | 0 |
| 24 | Qxb6 | 0 | Qe1+ | 0 |
| 25 | Ka2 | 0 | Bd5+ | 0 |
| 26 | b3 | 0 | Bxb3+ | 0 |
| 27 | cxb3 | 0 | Qxe2+ | 0 |
| 28 | Ka1 | 0 | Qe1+ | 0 |
| 29 | Ka2 | 0 | Qe2+ | 0 |
| 30 | Ka1 | 0 | Qe1+ | 0 |
Engine self-play
10 games at 500 000 nodes per move: White won 0, drawn 10, Black won 0 — White scored 50.0%. Average length 36.6 moves.
Sample game 1 (1/2-1/2)
1. b3 b5 2. f3 f5 3. g3 g6 4. Qxh8 Rxh8 5. e4 Bh6 6. Be3 Bxe3 7. Nxe3 e6 8. Nc3 Ne7 9. Ne2 Nf6 10. d3 Rf8 11. Kd2 c5 12. e5 Nfd5 13. f4 Nxe3 14. Kxe3 Bxh1 15. Rxh1 Rg8 16. h4 h6 17. c4 g5 18. hxg5 hxg5 19. fxg5 Rxg5 20. Rh8+ Rg8 21. Rxg8+ Nxg8 22. cxb5 Rxb5 23. Nc3 Ra5 24. Na4 c4 25. d4 cxb3 26. axb3 Ne7 27. Kd3 Nc6 28. Nc3 Ra6 29. Na4 Ra5 30. Nc3 Ra6 31. Na4
Sample game 2 (1/2-1/2)
1. g3 e6 2. a4 g5 3. Ndc3 h5 4. O-O-O h4 5. g4 h3 6. d4 Nf6 7. Qa2 Nxg4 8. d5 Qh6 9. dxe6 fxe6 10. Nd2 Bg7 11. Qb3 Nd6 12. Nde4 O-O 13. Nxd6 cxd6 14. Rxd6 Ne5 15. f4 b6 16. Bxa8 Rxa8 17. Nd5 Rae8 18. Bd4 Nf7 19. Bxg7 Qxg7 20. Rxd7 exd5 21. Rxd5 gxf4 22. Rxf4 Qg1+ 23. Rd1 Qe3+ 24. Qxe3 Rxe3 25. Rg1+ Kh7 26. Rgf1 Kg6 27. Rg1+ Kh5 28. Rf5+ Kh6 29. Rf4 Kh7 30. Rgf1 Rxe2 31. Rxf7+ Rxf7 32. Rxf7+ Kg6 33. Rf3 Rxh2 34. b4 Rh1+ 35. Kb2 Kh5 36. Rd3 Kg4 37. Rd4+ Kf3 38. Rd3+ Kg2 39. Rd2+ Kf3 40. Rd3+ Kg2
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 111 / 562 in the app's encyclopedia, then choose how to play.
- Local game — two players on one device, with a clock.
- With a mentor — a clearly labelled training bot with hints, at your level.
- Challenge a friend — an online game by link; both players get the same pair, colours swap on rematch.
Play this pair against the computer, right here Play a friend
FEN (Shredder, castling rights by rook files): brnknbrq/pppppppp/8/8/8/8/PPPPPPPP/QNRNKRBB w CFbg - 0 1
Mirror twin: White 848 vs Black 487 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 458.